Interesting question! I quote in extenso from a 1907's book titled "The rise and early constitution of universities, with a survey of mediæval education" (available here):
The term "universitas" had no connection with "universale," and did not, any more than the word "generale," carry with it any reference to the universality of the curriculum of study. This is now beyond all question. It was again and again formally applied by popes and kings to institutions which made no pretension to teach the circle of knowledge. Mr. Anstey scarcely exaggerates when he says that " vestra universitas" in a papal rescript may often be translated simply "all of you." In running over the works of John of Salisbury, I find a letter (cclxi.), written in 1168 to the Conventus of the Ecclesia Cantuariensis, which begins thus: "Universitati sanctorum qui in prima Britanniarum sede . . . Domino famulantur," etc. In fact, the term "universitas" was in the earlier part of the Middle Ages applied to towns or communia regarded as organized bodies; hence its application by John of Salisbury to a conventus. As applied to a studium, it simply meant a community, the word being in the course of time restricted to a learned community—a universitas literaria. We learned in a previous lecture that in Bologna the general universitas of students divided itself into two sections — the universitas ultramontanorum and the universitas citramontanorum. When the popes issued letters of privilege to an university, they addressed it (as did Frederick in the case of the University of Naples, founded by him) as a universitas (or community) doctorum et scholarium. Now, the mere epistolary recognition of these communities, by pope or monarch, as possessing certain privileges and internal rights of self-government, was practically their incorporation, and the term "universitas" thus gradually acquired the signification of "incorporated community," at about the same time that it began to be restricted to learned institutions.
The book itself looks very interesting and there is more context and discussion in pages around the quoted text. But the answer seems fairly clear: universitas was a term used to designate a community, and it is not related to universality (of topics of study, or of the unity of knowledge).